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THEOREiM 343 THEOSOPHY by a coxnrse of reasoning called a demon- stration. In the synthetical method of investigation, which is that for the most part employed in geometry, it is usual to state the principle to be proved before commencing the demonstration, which proceeds by a regular course of argu- mentation to the final conclusion, con- firmatory of the principle enunciated. The principle being proved, it may prop- erly be employed as a premise in the deduction of new truths. The principle, as enunciated before the demonstration, is the theorem; its statement after demonstration constitutes a rule or formula, according as the statement is made in ordinary or in algebraic lan- guage. A theorem differs from a problem in this, that the latter is a statement of something to be done, the former of something to be proved. THEORIA MOTUS, or THEORIA MOTUS CORPORTJM CCELESTIUM, the names by which is usually quoted the work of Gauss, in which he first showed the method of computing an orbit from three determinations of a planet's or comet's position, and thus rescued as- tronomers from the danger of losing the newly discovered asteroid Ceres after it had disappeared in the region of the sun. The full title of the work is "Theoria Motus Corporum Coelestium in Sectioni- bus Conicis Solum Ambientium." It was first published at Hamburg in 1809. An English translation by Rear-Admiral C. H. Davis, U. S. N., then superintendent of the Nautical Almanac OfSce, was pub- lished in Boston in 1857, at the joint ex- pense of the "Nautical Almanac" Office and the Smithsonian Institution. A French translation by Dubois was pub- lished at Paris in 1864, and a German one by Hasse at Hanover in 1865. The work also contains an exposition of the theory of the method of Least Squares, and is one of the most important astro- nomical works extant. THEOSOPHY, a name which since the time of Ammonius Saccas, in the 3d cen- tury after Christ, has been used in the West to cover various schools of relig- ious philosophy, which all unite in the fundamental conception that man, in his innermost nature, is a spiritual being, one in his essence with the Universal Spirit manifested in and through the uni- verse. In this general sense it includes mystics differing from one another in details. In the East the system now called Theosophy has been known for ages under the titles of Atma Vidya ("spirit science"), Brahma Vidya "sci- ence of Brahma"), Gupta Vidya "secret science"), and other similar names. All alike, in East and West, draw in- spiration and their methods from the "Wisdom Religion," the ancient esoteric philosophy. This claims among its initi- ates the men who have given to the world fragments of the teaching as ba- sis for world-religions, men like Buddha, Confucius, Zarathustra, Pythagoras, Plato, Jesus, and more ancient sages such as Manu, Narada, and other great Ri- shis. In the 16th century Paracelsus and Giordano Bruno are among its grandest exponents, and in our own day its mes- senger was a woman of Russian birth, Helena Petrovna Blavatsky (1831-1891). The Esoteric Philosophy, or Wisdom Religion, is a body of teaching, philosoph- ical, scientific, and religious, which is be- lieved to be preserved from generation to generation by a brotherhood of initi- ates scattered over the world, but pre- serving close and intimate relations with one another. To a group of these sta- tioned in Tibet the founding of the Theo- sophical Society in 1875 is ascribed, and they are constantly referred to in theo- sophical literature as Mahatmas, Arhats, Masters, Brothers, or Adepts. They are men who have evolved the spiritual na- ture till the physical body and brain con- sciousness have become ductile instru- ments for the spiritual intelligence. By virtue of this evolution they are said to have gained control over natural forces which enables them to bring about results that appear to be miraculous. This philosophy teaches as basic prin- ciples an eternal existence beyond hu- man cognition, existence per se, abso- luteness or "beness." A periodical as- pect of this is life, consciousness, mani- festing itself in and as the universe, pri- marily emanating as the dual root sub- stance, matter on its negative, and spirit, or energy, on its positive side. This duality is the note of the manifested universe, manifestation being held to be impossible without the "pairs of oppo- sites," positive-negative, active-passive, light-darkness, and the like, ultimating at one part of the chain of evolution in sex difference, male-female. Spirit and matter are therefore not separable, but are merely the opposed poles of the one root substance, and are present in every particle, as the poles in each fragment of a broken magnet. Evolution consists in the gradual densifying of the root substance through seven stages or planes of differentiated existence, the matter as- pect becoming more and more prominent as the evolution proceeds, and the spirit aspect becoming more and more hidden; thus matter reaches its fullest differenti- ation, evolving the whole of its capacities as a vehicle. From this point of com-